I implemented a setting to customize the intensity of the "static pixel shadows"! 

MRMOTRON DMG improvises this effect by blurring the input image and applying the resulting "shadows" only for the darker pixels (the ones that would actually cast the shadows) instead of utilizing "physical" separation of layers and "real" shadows, which would not be feasible in EEVEE. 

The result is pretty convincing, but these shadows are entirely "static", as in, they don't follow the scene lights.